what is the probability of getting exactly 2 blue bulbs?

Question

a batch of light bulbs contains 9 yellow, 5 green, 7 reds, and 4 blue bulbs. three different light bulbs are randomly selected from the batch (WITHOUT REPLACEMENT).

find the probability that exactly two bulbs are blue

tnx for da help^ ^

Answer 1

there are 25 bulbs. 4 of them are blue.

So the probablity of select the first blue bulb is 4/25.
AFter one bulb is selected, there are 24 bulbs left, out of which 3 are blue. That gives the probability of select a second blue bulb is 3/24.

Since the question ask for exactly 2 blue bulbs. The third blue must NOT be blue. There are 23 bulbs left and 21 bulbs are not blue. So the probablity of selecting a bulb that is not yellow is 21/23

since order does not matter, there are 3!/2! = 3 ways you can select the 3 bulbs

P = 3 (4/25) (3/24) (21/23)
P = 63/1150 <== answer

Answer 2

Yep. The probability is 3 times the probability of selecting in the exact order blue, blue, not-blue.

And the first answer shows you how to compute that.